波导中弹性波频散曲线计算的谱方法

发布时间：2018-12-12 09:51

【摘要】：将谱方法应用于平板和充水圆柱管中弹性波频散曲线的计算,采用Chebyshev插值和微分矩阵把本征方程离散为一系列线性方程.将超越方程搜根问题转化为广义本征值求解问题,求得的本征值即为波数,改变频率进而获得弹性波频散曲线.计算算例表明,与搜根方法相比,该方法回避了大量特殊函数的计算,因而计算速度更快并且更易实现;将此方法得到的频散曲线与搜根方法的结果进行比较,证明该方法是合理的、可行的.
[Abstract]:The spectral method is applied to the calculation of elastic wave dispersion curves in flat and water-filled cylindrical tubes. The intrinsic equations are discretized into a series of linear equations by Chebyshev interpolation and differential matrix. The root search problem of transcendental equation is transformed into a generalized eigenvalue problem. The obtained eigenvalue is wavenumber. The frequency is changed and the elastic wave dispersion curve is obtained. The calculation examples show that the method avoids the calculation of a large number of special functions compared with the root search method, so it is faster and easier to implement. The results of the dispersion curve obtained by this method are compared with the results of the root search method, and it is proved that the method is reasonable and feasible.
【作者单位】：上海交通大学高新船舶与深海开发装备协同创新中心海洋工程国家重点实验室;勒芒大学声学实验室;
【基金】：青年科学基金项目(11504233)资助
【分类号】：O347.41

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